(x-4)(x-6)=18

Solution for (x-4)(x-6)=18 equation:

(x-4)(x-6)=18

We move all terms to the left:

(x-4)(x-6)-(18)=0

We multiply parentheses ..

(+x^2-6x-4x+24)-18=0

We get rid of parentheses

x^2-6x-4x+24-18=0

We add all the numbers together, and all the variables

x^2-10x+6=0

a = 1; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·1·6
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*1}=\frac{10-2\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*1}=\frac{10+2\sqrt{19}}{2}
$